Gravitational Redshifts: Main Sequence vs. Giants

One of the consequences of Einsteins theories of relativity is that everything will be affected by gravitational potentials, regardless of their mass. The effect of this is observed in experiments demonstrating the potential for gravity to bend light. But a more subtle realization is that light escaping such a gravitational well must lose energy, and since energy for light is related to wavelength, this will cause the light to increase in wavelength through a process known as gravitational redshifting.

Since the amount of redshift is dependent on just how deeply inside a gravitational well a photon is when it starts its journey, predictions have shown that photons being emitted from the photosphere of a main sequence star should be more redshifted than those coming from puffed out giants. With resolution having reached the threshold to detect this difference, a new paper has attempted to observationally detect this difference between the two.

Historically, gravitational redshifts have been detected on even more dense objects such as white dwarfs. By examining the average amount of redshifts for white dwarfs against main sequence stars in clusters such as the Hyades and Pleiades, teams have reported finding gravitational redshifts on the order of 30-40 km/s (NOTE: the redshift is expressed in units as if it were a recessional Doppler velocity, although it’s not. It’s just expressed this way for convenience). Even larger observations have been made for neutron stars.

For stars like the Sun, the expected amount of redshift (if the photon were to escape to infinity) is small, a mere 0.636 km/s. But because Earth also lies in the Sun’s gravitational well the amount of redshift if the photon were to escape from the distance of our orbit would only be 0.633 km/s leaving a distance of only ~0.003 km/s, a change swamped by other sources.

Thus, if astronomers wish to study the effects of gravitational redshift on stars of more normal density, other sources will be required. Thus, the team behind the new paper, led by Luca Pasquini from the European Southern Observatory, compared the shift among stars of the middling density of main sequence stars against that of giants. To eliminate effects of varying Doppler velocities, the team chose to study clusters, which have consistent velocities as a whole, but random internal velocities of individual stars. To negate the latter of these, they averaged the results of numerous stars of each type.

The team expected to find a discrepancy of ~0.6 km/s, yet when their results were processed, no such difference was detected. The two populations both showed the recessional velocity of the cluster, centered on 33.75 km/s. So where was the predicted shift?

To explain this, the team turned to models of stars and determined that main sequence stars had a mechanism which could potentially offset the redshift with a blueshift. Namely, convection in the atmosphere of the stars would blueshift material. The team states that low mass stars made up the bulk of the survey due to their number and such stars are thought to undergo greater amounts of convection than most other types of stars. Yet, it is still somewhat suspect that this offset could so precisely counter the gravitational redshift.

Ultimately, the team concludes that, regardless of the effect, the oddities observed here point to a limitation in the methodology. Trying to tease out such small effects with such a diverse population of stars may simply not work. As such, they recommend future investigations target only specific sub-classes for comparison in order to limit such effects.

By Jon Voisey
-
Jon is a science educator currently living in Missouri. He is a high school teacher and does outreach with the St. Louis Astronomical society as well as presenting talks on science and related topics at regional conventions. He graduated from the University of Kansas with his BS in Astronomy in 2008 and has maintained the Angry Astronomer blog since 2006.
For more of his work, you can find his website here.

8 Responses

Mysterious. The bulk of the dispersing photons starts out with absorption lines acquired in the equivalent deeper well, but I take it they are thermalized making the photosphere the imprinter of those lines. [The paper, modulo I misunderstood the technical terms, seems to say that the depth of acquisition somewhat depends on wavelength as would then be expected.]

I note that there are a lot of small discrepancies between the model and the observations, making it even more suspect. In fact they seem to me to accept it not because it fits well or isn’t suspect, but because it is the one hypothesis they can come up with. Well, it is a start for eventually making an explanation, if perhaps a wrong turn.

Small nitpick: the Sun-Earth description is a good one, but the next paragraph “Thus …” is not explicitly supported by it and referencing it in toto. Such illogical text constructions is the type that IMHO makes it hardest for those most reaching for the decoding to understand. If you have a minimum sense of what is said you can bridge the gap/leave the hiccup behind you, if not they become a stumbling block for attaining precisely that minimum sense.

I found this to be difficult to read as well. I was not aware that people looking at gravitational redshift in stars expressed it as equivalent to velocity Doppler shift. It should be expressed according to z written according to the delay coordinates of the Schwarzschild metric. Further, I find it difficult to see how convection from the surface results in a net blue shifting. The material would have to be streaming away from the star. If it at all falls back down this would be a redshifting, which I think with the blue shifting would result in a spectral broadening,

Interesting comments, but sorry guys, your slightly wayward thinking because you are considering it like like cosmologists instead of more straight forward stellar evolutionists!.

I do suggest that you might like to read the very useful on-line 1996 article By von Tipple entitled; Main Sequence Masses and Radii from Gravitational Redshifts; which is taken from the letters from the Astrophysical Journal, 438, L37. Gravitational redshift is mostly given as ‘g’ or preferably “log g” (though sometimes this is K, which I thought wasn’t suggest to use because it might be confused with K-type stars! (The linked paper uses ‘K’.) It is akin to small time dilation effect in a gravity well. Sources, like the FK4 and FK5 (and FK6) Star catalogues have it expressed in their tables.
This methods builds n top of the main sequence stars; expressing the differential between them and the giant stars — though the principal is just the same. The biggest is to get precision spectroscopy and rely on as the link paper sugges; then in turn, using this data to generate the secondary parameters of temperature, mass and radii; to find the value of the gravitational redshift ‘log g’. (If I can remember, it is log g, only because luminosity of all stars is often expressed in solar terms as log too!)
Measure of gravitation redshift is measured as K=0.635 x (M/R) being in solar terms; so it heavily relies on knowing the masses and radii; the latter being less well known.

As to this article, I am a little confused as why it is “news.” Other studies have always used star clusters to see the distribution of gravitational redshifts, which there are many studies.Usually some interest has been with white dwarfs in the nearby cluster (like the Pleiades as imaged) as the shifts are significant large. One of the issues is there are not many giant stars in clusters; so I’m not sure what Pasquini is exactly doing here.

It is interesting that their study mostly focusses on M67 in Cancer, which is about 2 billion years old and has several prominent giant stars.

It seems that the first comparison between main sequence and giant strs, as this story eludes to, is stated by Pasquini,, et.al here, which I didn’t know.,

One hint came from a study of the open cluster NGC 3680 by Nordstrom et al. (1997), who found the giants (though the sample contained only six such stars) to be blueshifted on average 0.4 km s^?1 relative to the dwarfs, as expected from gravity.

Also the conclusion of this paper nicely sums up the continued considerable difficulties in the advancement of measuring these gravitational redshifts, and seemingly unchanged for the last few decades. (This backs up my previous comments too). They say;

Not many current spectrometers have adequate performance for such tasks, but work is in progress towards realizing such high-fidelity spectroscopy with an accurate wavelength calibration at the largest telescopes. With these instruments it will be possible to extend the present study to less explored stars, for instance in the metal-poor and in the metal-rich regimes.

As commenting for the techniques expressed in von Hipple (in my earlier post), they agreeably say;

This study thus also illustrates the limitations of cross- correlation techniques for high-accuracy lineshift measurements. To understand the origin of wavelength shifts that are only a small fraction of any spectral-line width, a cross-correlation measure over an extended spectral range may not be adequate…

NOTE: UT Readers might like to look at the Introduction of Pasquini,, et.al. paper. (Sections 1.1 and 1.2) This has an excellent summary of the history of gravitational redshifts, which is stated in better words than mine or Jon’s.

Well, I must confess I generally see astronomy, if not from a cosmological view, as top-down, coming from the outside with some physics background. In fact, I’m taking an astrobiology course, and the young stars, planetary systems and differentiated terrestrials are my first bottom-up subjects! But no main sequence stuff (I had to skip precisely that voluntarily part, my own main sequence took precedence. :-o)

But in my previous comment I don’t think you can’t see any of that unless you read that into it. I’m mainly puzzled about the photosphere workings. Also, I would never presume to claim how anyone “should” express (sorry LC!) their measurements I hope, even though I once was confused over the time references astronomers used over at Bad Astronomy (counting age from observation frame, not object frame). Unless it’s about SI units, there I’m vocal! 😮

Tiny wavelength shifts of spectral lines may be caused by a variety of effects (which is indeed the reason why it is challenging to uniquely identify gravitational redshifts in ordinary stars). Most spectral lines from the Sun and ordinary stars show a small overall blueshift that is caused by the mixture of gas clouds of different temperature across the stellar surface (the “granulation” pattern). Some gas clouds are hotter and therefore glow brighter, others are cooler and fainter. The hot ones are rising upwards (carrying up heat from the stellar interior): spectral lines arising in those particular clouds become blueshifted because the clouds are moving up and approaching the observer. When rising up through the stellar atmosphere, the gas clouds gradually cool off and then sink down again. Now the spectral lines in these sinking and cooler clouds instead become redshifted since their motion is down and away from the observer. On the solar surface, these patterns can be studied in some detail but for other stars one can only measure the average over all such clouds across the stellar surface. The averaged spectral lines become somewhat blueshifted – not because there is any gas leaving the star – but because the hot, bright, and rising clouds are more visible and contribute more blueshifted light than the same gas when it has cooled, is darker, sinking and redshifted. This effect, the so-called convective blueshift, is actually a tool that is used to examine detailed models of radiation interacting with gas motions near stellar surfaces.